Question

Select the correct answer.

Stephanie is exploring the key features of the functions ƒ (z) = and g(z) = 4=+5
She says that the graphs of the two functions will have the same vertical asymptote but different horizontal asymptotes because she ca
define function g as a transformation of function f and g(x) = f(x) + 4. Which statement is true?
O A. Stephanie correctly rewrote g(x) as a transformation of f(x), and she described the asymptotes of the two functions
correctly.
OB. Stephanie correctly rewrote g(x) as a transformation of f(x), but she described the asymptotes of the two functions
incorrectly.
OC. Stephanie rewrote g(x) as a transformation of f(x) incorrectly, but she described the asymptotes of the two functions
correctly.
O D. Stephanie rewrote g(x) as a transformation of f(x) incorrectly, and she described the asymptotes of the two functions
incorrectly.

Answer 1

A. Stephanie correctly rewrote g(x) as a transformation of f(x), and she described the asymptotes of the two functions correctly.

Explanation:

The statement is true because, g(x) = f(x) + 4 is indeed a transformation of f(x) by shifting the graph 4 units up, and because the horizontal asymptote is determined by the highest degree term in the function, which in this case is the same for both functions, so the two functions will have the same vertical asymptote, but the horizontal asymptote is determined by the leading coefficient which is different for both functions, so the two functions will have different horizontal asymptotes.